Abstract
The glass transition and related dynamics of two types of multilayered thin films were investigated using differential scanning calorimetry and dielectric relaxation spectroscopy, to clarify the nature of heterogeneous dynamics in thin polymer films. First, the \(\alpha \)-process of multilayered thin films of poly(2-chlorostyrene) (P2CS) and polystyrene (PS) with various geometries was investigated during annealing process. The relaxation rate of the P2CS layer increases near the upper electrode with annealing, while that near the bottom electrode remains almost constant or slightly decreases with annealing. The relaxation strength for the \(\alpha \)-process of the P2CS layer increases with annealing near the upper electrode, while it decreases near the bottom electrode. A distinct positional dependence of the \(\alpha \)-process could be observed in the multilayered films. Second, the glass transition temperature, \(T_\mathrm{g}\), and the dynamics of the \(\alpha \)- and \(\beta \)-processes for stacked thin films of poly(methyl methacrylate) (PMMA) were investigated during the annealing process. The \(T_\mathrm{g}\) and the dynamics of the \(\alpha \)-process of as-stacked PMMA thin films exhibit thin-film-like behavior. Annealing at high temperature causes the \(T_\mathrm{g}\) to increase from the reduced value, and causes the dynamics of the \(\alpha \)-process to become slower approaching those of the bulk. Contrary to the \(\alpha \)-process, the relaxation time of the \(\beta \)-process is almost equal to that of the bulk PMMA, and is unaffected by the annealing process. The fragility index increases with annealing, which suggests that the glassy state of the stacked thin films changes from strong to fragile.
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Abbreviations
- Al:
-
Aluminum
- \(\alpha _{ps}\) :
-
Shape parameter of dielectric spectrum of PS
- \(\alpha _{p2cs}\) :
-
Shape parameter of dielectric spectrum of P2CS
- \(\beta _{ps}\) :
-
Shape parameter of dielectric spectrum of PS
- \(\beta _{p2cs}\) :
-
Shape parameter of dielectric spectrum of P2CS
- \(\beta _{K}\) :
-
Stretching parameter of KWW function
- \(C^*\) :
-
Complex electric capacitance
- \(C'\) :
-
Real part of \(C^*\)
- \(C''\) :
-
Imaginary part of \(C^*\)
- \(C^*_{ps}\) :
-
Complex electric capacitances of PS layer
- \(C^*_{p2cs}\) :
-
Complex electric capacitances of P2CS layer
- DRS:
-
Dielectric relaxation spectroscopy
- DSC:
-
Differential scanning calorimetry
- \(d\) :
-
Thickness
- \(\varDelta C_{ps}\) :
-
\(\varDelta \varepsilon _{ps}\) multiplied by geometrical capacitance of PS
- \(\varDelta C_{p2cs}\) :
-
\(\varDelta \varepsilon _{p2cs}\) multiplied by geometrical capacitance of P2CS
- \(\varDelta \varepsilon _{\alpha }\) :
-
Dielectric relaxation strength of \(\alpha \)-process
- \(\varDelta \varepsilon _{\beta }\) :
-
Dielectric relaxation strength of \(\beta \)-process
- \(\varDelta \varepsilon _{ps}\) :
-
Dielectric relaxation strength of \(\alpha \)-process of PS
- \(\varDelta \varepsilon _{p2cs}\) :
-
Dielectric relaxation strength of \(\alpha \)-process of P2CS
- \(\varDelta T_{\alpha }\) :
-
Width of dielectric loss peak of \(\alpha \)-process
- \(\varDelta T_{\beta }\) :
-
Width of dielectric loss peak of \(\beta \)-process
- \(\varDelta T_{\beta }^l\) :
-
Value of low temperature side of \(\varDelta T_{\beta }\)
- \(\varDelta T_{\beta }^r\) :
-
Value of high temperature side of \(\varDelta T_{\beta }\)
- \(\varepsilon ^*\) :
-
Complex dielectric constant
- \(\varepsilon '\) :
-
Real part of \(\varepsilon ^*\)
- \(\varepsilon ''\) :
-
Imaginary part of \(\varepsilon ^*\)
- \(\varepsilon ''_\mathrm{max}\) :
-
Peak height of dielectric loss of \(\alpha \)-process
- \(\varepsilon _0\) :
-
Permittivity of a vacuum
- \(\varepsilon ^*_{ps}\) :
-
Complex dielectric constant of PS layer
- \(\varepsilon _{p2cs}^*\) :
-
Complex dielectric constant of P2CS layer
- \(\varepsilon _{ps,\infty }\) :
-
Dielectric permittivity at very high frequency of PS
- \(\varepsilon _{p2cs,\infty }\) :
-
Dielectric permittivity at very high frequency of P2CS
- \(f\) :
-
Frequency of applied electric field
- \(f_{\alpha }\) :
-
Relaxation rate of \(\alpha \)-process
- \(f_{\beta }\) :
-
Relaxation rate of \(\beta \)-process
- \(f_\mathrm{g}\) :
-
Relaxation rate of \(\alpha \)-process at \(T_\mathrm{g}\)
- \(f_\mathrm{max}\) :
-
Peak frequency at which dielectric loss shows a maximum
- HN eq.:
-
Havriliak-Negami equation
- KWW:
-
Kohlrauch-Williams-Watts relaxation function
- \(k_{B}\) :
-
Boltzmann constant
- LCST:
-
Lower critical solution temperature
- \(\ell \) :
-
Total thickness
- \(\ell _{ps}\) :
-
Thickness of PS layer
- \(\ell _{p2cs}\) :
-
Thickness of P2CS layer
- \(M_\mathrm{w}\) :
-
Weight-averaged molecular weight
- \(M_\mathrm{n}\) :
-
Number-averaged molecular weight
- \(m\) :
-
Fragility index
- \(\mu \) :
-
Effective dipole moment
- \(N\) :
-
Number density of relaxing dipoles
- P2CS:
-
Poly(2-chlorostyrene)
- PS:
-
Polystyrene
- PMMA:
-
Poly(methyl methacrylate)
- \(R\) :
-
Equivalent electrical resistance in sample
- \(S\) :
-
Area of electrode
- \(\sigma _{dc}\) :
-
Electric conductivity
- \(t_a\) :
-
Effective annealing time
- \(\tau \) :
-
Characteristic time of temporal change in \(T_{\alpha }\)
- \(\tau _{\alpha }\) :
-
Relaxation time of \(\alpha \)-process
- \(\tau _\mathrm{g}\) :
-
Relaxation time of \(\alpha \)-process at \(T_\mathrm{g}\)
- \(\tau _{ps}\) :
-
Relaxation time of \(\alpha \)-process of PS
- \(\tau _{p2cs}\) :
-
Relaxation time of \(\beta \)-process of P2CS
- \(\tau _{K}\) :
-
Relaxation time of KWW function
- \(T_a\) :
-
Annealing temperature
- \(T_{\alpha }\) :
-
Temperature at which the dielectric loss shows a peak due to \(\alpha \)-process
- \(T_{\beta }\) :
-
Temperature at which the dielectric loss shows a peak due to \(\beta \)-process
- \(T_\mathrm{g}\) :
-
Glass transition temperature
- \(T_{\alpha }^0\) :
-
Initial value of \(T_{\alpha }\)
- \(T_{\alpha }^{\infty }\) :
-
Final value of \(T_{\alpha }\)
- \(T_{V}\) :
-
Vogel temperature
- \(U\) :
-
Apparent activation energy
- VFT law:
-
Vogel-Fulcher-Tammann law
- \(\phi (t)\) :
-
Relaxation function
- \(\omega \) :
-
Angular frequency
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Acknowledgments
This work was supported by a Grant-in-Aid for Scientific Research (B) (No. 25287108) and Exploratory Research (No. 25610127, No. 23654154) from the Japan Society for the Promotion of Science. The authors would like to thank Prof. Friedrich Kremer for giving them an opportunity to publish the present article in this book. One of the authors (KF) would like to express his cordial thanks to Dr. Didier Long for giving him an opportunity to stay in his laboratory in Lyon as a visiting professor of CNRS, where half of the present article has been written.
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Fukao, K., Takaki, H., Hayashi, T. (2014). Heterogeneous Dynamics of Multilayered Thin Polymer Films. In: Kremer, F. (eds) Dynamics in Geometrical Confinement. Advances in Dielectrics. Springer, Cham. https://doi.org/10.1007/978-3-319-06100-9_8
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